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Abstract
On page 245, lines 3 and 4, of the published paper, we find the following text: “Since tr{UdΓ} can be expressed as the trace of the product of two positive definite matrices, tr{UdΓ} > 0, and thus cd > 0;” This text should be replaced with: “Since tr{UdΓ} can be expressed as the trace of a positive definite matrix, tr{UdΓ} > 0, and thus cd > 0;” The uncorrected text claims that Ud and Γ are positive definite matrices, but Ud can’t be positive definite, since its rank (difference between the ranks of the derivatives of the two models involved) is much less than its order. The expression tr{UdΓ} could be written differently so that the conclusion still holds. Namely, write Ud = VΠP−1 A′ (AP−1 A′ )−1 AP−1 Π′ V (formula (4) of the paper) as Ud = FF′ , where F = VΠP−1 A′ (AP−1 A′ )−1/2 ; then, tr{UdΓ} = tr{FF′ Γ} = tr{F′ ΓF}, where F′ ΓF is a positive definite matrix, given that Γ is positive definite in the setup of the paper. For rewriting the alternative expression of tr{UdΓ}, we used the well-known matrix algebra result that tr{MN} = tr{NM} for matrices M and N of dimensions conformable with the products; in our application, M = F and N = F′ Γ.
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